Self-guided beams in a diffractive χ⁽²⁾ medium: variational approach

It is demonstrated that the (1+1)- and (2+1)-dimensional self-guided beams (two-wave parametric spatial solitons) in a diffractive dielectric medium with purely quadratic nonlinearity (the so-called χ⁽²⁾ material) can be effectively approximated by means of a familiar variational approach. In particular, for the physical conditions for which no analytical solutions exist, the variational approach yields Gaussian approximations of the (1+1) beams such that the ratio of the harmonic energy to the total beam energy equals, with ∼ 0.1% error, to the ratio obtained numerically.